Answer
Converges
Work Step by Step
Apply the root test to the series
$\Sigma^{\infty} _{n=1} \frac{1}{5^n} $
$\lim\limits_{n \to \infty} \sqrt[n] {|\frac{1}{5^n}|} $, Absolute values fall out because all values are positive
$\lim\limits_{n \to \infty} \frac{1}{5} = \frac{1}{5}<1$
Because the answer is less than 1, the series converges
